1. Field of the Invention
The present invention relates in general to systems for measuring scattering parameters (xe2x80x9cS-parametersxe2x80x9d) of an electronic network having wideband input and output signals, and in particular to a system for measuring S-parameters of a non-linear, wideband network.
2. Description of Related Art
FIG. 1 is a simple block diagram of a two-port active or passive electronic network 10 such as an amplifier or a filter supplying an output signal of current I2 and voltage V2 to a load of impedance ZL at its output port (P2) in response to a sine wave input signal of current I1 and voltage V1 supplied to its input port (P1) from a signal source 12. Port P1 can reflect a portion of that input signal back towards its source 12 depending on the amount of mismatch between the output impedance of signal source 12 and the network""s input impedance. The reflected signal""s amplitude increases with the impedance mismatch, and when the network""s input impedance perfectly matches the signal source""s output impedance there will be no reflection at all. Similarly, load impedance ZL will reflect some portion of the network""s output signal back towards port P2 depending on how well the network""s output impedance matches the load impedance. Amplifier 10 will also feed back some of the reflected load signal to port P1, a process known as xe2x80x9creverse gainxe2x80x9d.
A circuit designer normally doesn""t want any signal reflections because they impede power transfer in the output signal. To reduce reflections, the designer usually tries to design a multi-port network so that its input impedances match the expected output impedances of the circuits that are to supply its input signals, and so that the network""s output impedances match the impedances of its anticipated loads. For high frequency applications, designers typically design circuit components so that they each have a standard input/output impedance, usually called xe2x80x9cZ0xe2x80x9d. 50 Ohms is a commonly employed impedance standard for radio frequency circuits.
Thus when designing a network such as an amplifier, a circuit designer wants not only to be able to predict the network""s forward gain, but also wants to predict how much of its input and output signals will be reflected when the network is operating in a standard Z0 impedance environment. The designer will also want to know the network""s reverse gain.
Circuit designers often use a scattering parameter (xe2x80x9cS-parameterxe2x80x9d) model to describe the behavior of a two-port or multi-port network. FIG. 2 is a conventional S-parameter model of the two-port network 1 of FIG. 1. The model is called a xe2x80x9cscattering parameterxe2x80x9d (S-parameter) model because it takes into account signal reflections (scattering) of the network""s input and output signals. The S-parameter model represents the incoming and reflected signals at port P1 by waveform parameters a1 and b1, represents the outgoing signal at port P2 by a waveform parameter b2 and represents the signal reflected from the load back toward the port P2 as a waveform parameter a2. The following four relations define the a1, b1, a2 and b2 parameters in terms of the network""s input and output voltages and currents:
a1=(V1+Z0I1)/2(Z0)xc2xdxe2x80x83xe2x80x83[1]
b1=(V1xe2x88x92Z0I1)/2(Z0)xc2xdxe2x80x83xe2x80x83[2]
a2=(V2+Z0I2)/2(Z0)xc2xdxe2x80x83xe2x80x83[3]
b2=(V2xe2x88x92Z0I2)/2(Z0)xc2xdxe2x80x83xe2x80x83[4]
The network model includes a set of S-parameters S11, S21, S12 and S22 representing the behavior of the network. The input reflection coefficient S11, a function of the network""s input impedance, models how the network reflects the input signal in an Z0 environment. When the network""s input impedance matches Z0, the S11 parameter will be 0. The S21 parameter is the insertion gain of the network when it is operating in a Z0 environment. An xe2x80x9coutput reflection coefficientxe2x80x9d S22, a measure of signal reflection at port P2, is a function of the network""s output impedance in relation to Z0. S22 has zero value when the network""s output impedance matches Z0. The S12 parameter is a measure of the network""s reverse gain. The S-parameter model relates the a1, b1, a2, and b2 waveforms to the S11, S12, S21, and S22 S-parameters as follows:
b1=S11a1+S12a2xe2x80x83xe2x80x83[5]
b2=S21a1+S22a2xe2x80x83xe2x80x83[6] 
When the expected performance of a network design is specified in terms of the S-parameter model, a designer can use readily available computer-aided design tools to compute the S-parameters of a network design to determine how well the design meets its S-parameter specifications. After the network is fabricated, a test engineer would like to be able to measure the network""s actual S-parameter values to determine whether the network meets those specifications. Since the S-parameters are an abstraction the test engineer cannot measure them directly, but he or she can compute them from signal measurements made at the network""s input and output terminals as it drives a Z0 load in response to an input sine wave signal produced by a signal source having a Z0 output impedance.
FIGS. 3 and 4 illustrate one way to measure the S-parameters of network 10 of FIG. 1. With port P2 terminated with the network""s characteristic impedance Z0 and source 12 driving port P1 as illustrated in FIG. 3, there will be no incident wave a2 at port P2 because there will be no reflection at the load. With a2 equal to 0, equations [5] and [6] reduce to:
b1=S11a1xe2x80x83xe2x80x83[7]
b2=S21a1xe2x80x83xe2x80x83[8]
By measuring the a1, b1, and b2 waves, with the test configuration of network 10 we can solve equations [7] and [8] to compute the S11 and S21 parameters.
We then terminate port P1 with characteristic impedance Z0 so that there is no incident wave a1 at that port and use signal generator 12 to stimulate port P2. With a1 equal to 0, equations [5] and [6] reduce to:
b1=S12a2xe2x80x83xe2x80x83[9]
b2=S22a2xe2x80x83xe2x80x83[10]
Thus by measuring the a2, b1, and b2 waves, with the test configuration of network 10 we can solve equations [9] and [10] to compute the S12 and S22 parameters.
Unfortunately the S-parameter measurement approach described above is not highly accurate because it does not account for errors resulting from the influences of the internal impedances of the test system that must be connected to network 10 when measuring a1, a2, b1 and b2.
FIGS. 5A and 5B depict a test system 14 typically used to measure the a1, a2, b1 and b2 values needed to determine the S-parameters of a two-port (network) network under test 16. FIG. 5A shows the test system 14 configured to make the forward measurement depicted in FIG. 3 and FIG. 5B shows test system 14 configured to make the reverse measurement depicted in FIG. 4. Test system 14 includes a signal generator 18 supplying a single-frequency test sine wave signal to the network""s port P1 and a load impedance Z0 connected to port P2. A directional coupler 20 senses the incident and reflected signals at port P1 and delivers voltage waveforms a1m and b1m to a data acquisition and processing (DAP) system 24. A similar directional coupler 22 senses the output and reflected signals at port P2 and delivers to DAP 24 voltage waveforms b2m and a2m.
The a1m, b1m a2 and b2 waveforms DAP system 24 senses are not directly proportional to the a1, b1, a2 and b2 waveforms appearing at ports P1 and P2 because directional couplers 20 and 22 have impedances that alter the incident and reflected waves and that can cause additional signal reflections. Systematic errors result from signal leakages due to directivity (D) and cross-talk (X), from source (S) and load (L) impedance mismatches, and from frequency response errors caused by reflection (R) and transmission tracking (T) within DAP system 24.
FIG. 6 models test system 14 of FIG. 5A when it is making a xe2x80x9cforward measurementxe2x80x9d of network 10 with signal generator 18 driving port P1 as in FIG. 3. FIG. 7 models test system 14 of FIG. 5B when it is making a xe2x80x9creverse measurementxe2x80x9d of network 10 with signal generator 18 driving port P2 as in FIG. 4. In addition to the S11, S12, S21 and S22 S-parameters modeling network 10, the model of FIG. 6 includes a set of six xe2x80x9cerror parametersxe2x80x9d (E-parameters) ED, ES, ER, ET, EL, and EX, each modeling a separate one of the six sources of test system error during forward measurements. Similarly FIG. 7 includes six additional E-parameters EDxe2x80x2, ESxe2x80x2, ERxe2x80x2, ETxe2x80x2, ELxe2x80x2, and EXxe2x80x2, each modeling a separate source of test system error during reverse measurements.
To more accurately determine the values of the network""s S-parameters, DAP system 24 must first determine the values of its own E-parameters and then account for the influence of those E-parameters when computing S-parameters based on the forward and reverse measurements. It is therefore customary to perform a set of calibration measurements of the a1m, b1m, a2m and b2m parameters from which all 12 E-parameter values are computed. With the values of the E-parameters known, the network""s actual S-parameter values can be computed from the E-parameter values and uncorrected S-parameter values determined when network 10 is thereafter tested as discussed above in connection with in FIGS. 3 and 4. Formulas for such computations are well-known. See for example, the document xe2x80x9cApplying Error Correction to Network Analyzer Measurementxe2x80x9d, Hewlett Packard Application Note 1287-3 published in 1997, incorporated herein by reference.
FIGS. 8-15 depict test setups for a series of eight calibration measurements that are typically used to determine the forward and reverse E-parameters. In the tests of FIGS. 8-10, signal generator 18 supplies a stimulus to the input port of directional coupler 20 while its output port is terminated through Z0 (FIG. 8), shorted to ground (FIG. 9) or open-circuited (FIG. 10). It is well-known that values of error parameters ED, ES and ER of FIG. 6 can be computed from measurements of a1m and b2m DAP system 24 makes during those three tests. FIGS. 11-13 illustrate a similar set of tests carried out on directional coupler 22. Values of error parameters EDxe2x80x2, ESxe2x80x2 and ERxe2x80x2 of FIG. 7 are computed from measurements of a2m and b2m DAP system 24 makes during those three tests. In the test setups of FIGS. 14 and 15, the two directional couplers 20 and 22 are interconnected. In FIG. 14 source 18 sends an a sine wave signal to directional coupler 20 while a port of directional coupler 22 is terminated by Z0. In FIG. 15 source 18 sends the sine wave signal to directional coupler 22 while a port of directional coupler 20 is terminated by Z0. The remaining E-parameters of FIGS. 6 and 7 can then be computed from the known values of ED, ES, ER, EDxe2x80x2, ESxe2x80x2 and ERxe2x80x2 and the measured values of a1m, b1m, a2m and b2m waveform measurements acquired during the tests illustrated in FIGS. 14 and 15.
Thus in order to determine the S-parameter values of network 10, is it customary to carry out the following steps:
1. make a series of calibration measurements as illustrated in FIGS. 8-15 to first determine the E-parameter values,
2. compute the E-parameter values for the test system,
3. perform forward and reverse tests of the network 10,
4. calculate uncorrected S-parameter values for the network based on the forward and reverse tests, and
5. apply error correction formulas to produced error corrected S-parameter values based on the computed E-parameter and uncorrected S-parameter values.
A network""s S-parameters are functions of input signal frequency because a network""s forward and reverse gains and the reflections at its input and output ports are functions of input signal frequency. The test system""s E-parameter values are also functions of input signal frequency. Hence all of the test and calibration configurations of FIGS. 3, 4 and 8-15 employ a signal source 18 generating the same single frequency sine wave output signal. When the network 10 is expected to operate with a single-frequency sine wave input signal, then the designer need only design the network to operate at that frequency and need only specify the network""s S-parameters for that frequency. Thus it is necessary to determine only the values of the E-parameters and S-parameters for that particular operating frequency.
However when a network is expected to operate at several different frequencies, designers specify the network""s S-parameter values for each of the several frequencies of interest. Thus when testing networks that can operate at any of several frequencies, the test engineer must determine whether the network""s S-parameter values meets such specifications for each specified frequency of interest. Since the measurement system""s E-parameters are also functions of signal frequency, the test engineer will have to determine the system""s E-parameter values for each frequency of interest before computing the network""s S-parameters. Accordingly it is customary to repeat the entire prior art E-parameter and S-parameter measurement and calculation process for each single frequency of interest.
Some networks are designed to amplify a wideband modulated input signal that is the sum of two or more components of differing frequency. Design engineers separately specify the desired S-parameter values for each frequency component and prior art S-parameter measurement systems test such networks the same way they test networks that are expected to respond separately to each of several single-frequency input signals; they simply repeat the prior art single-frequency E-parameter calibration and S-parameter measurement process for each single-frequency of interest that may be included as a component of the wideband input signal. In such case signal generator 18 is often a sweep generator capable of stepping its output signal frequency over the frequency range including all frequencies of interest. During each calibration or network test, DAP system 24 acquires waveform data at each frequency step of interest, and then computes the E-parameters and S-parameters for each frequency of interest from the data acquired while signal generator 18 was operating at that frequency.
Such an S-parameter measurement approach for a network that is to receive a wideband stimulus is valid when the network is to operate in a linear region. In a linear network, each frequency component of an output signal is a function only of an input component of the same frequency. A linear network""s S-parameter are not functions of the magnitude of any input signal component. Accordingly, when we stimulate a linear network with a wideband input signal having N different frequency components, it will not only produce an output signal having N components of similar frequency, each output signal frequency component will look exactly as if the network had amplified the corresponding input signal component as a single frequency input signal rather than as one component of a wideband signal. Thus for each given frequency, a linear network will have the same S-parameter values relative to that frequency regardless of whether it is being stimulated by a single sine wave of that particular frequency or by a wideband signal having that particular frequency as just one component. The test engineer can therefore be confident that when he/she separately determines the S-parameters for each frequency of interest in the manner described above, those S-parameters vales will fairly represent the behavior of a linear network with respect to each signal component when it is stimulated with the wideband signal.
However not all networks are expected to operate as linear networks. For example cellular telephone amplifiers producing radio frequency output signals are often designed to operate at the upper limit of their linear ranges to conserve battery power. Such a cellular telephone amplifier can sometimes be driven into their non-linear operating ranges when various components of their wideband input signal happen to peak concurrently. Hence to determine how a telephone might behave under such conditions, a test engineer would like to measure amplifier S-parameters indicating not how such an amplifier responds to each individual component of a wide band signal, but indicating how the amplifier responds to each signal component of a wideband input signal that can overdrive the amplifier into its non-linear operating range.
The prior art approach of separately measuring the frequency-dependent S-parameters values for each component of interest of a network receiving a wideband input signal loses its validity when the wideband signal drives the network into its non-linear operating range. Under such circumstances, the amplitude of each frequency component can affect how the network responds to every other frequency component. The prior art xe2x80x9cmultiple single-frequencyxe2x80x9d approach to S-parameter measurement fails to produce S-parameter values accurately reflecting how a non-linear network behaves in response to a wideband signal.
The present invention relates to a test system for measuring scattering parameters (S-parameters) characterizing the behavior of a multi-port network that is driven into a non-linear operating region by a wideband signal having components of more than one frequency.
In accordance with one aspect of the invention, the test system includes a signal generator for producing the wideband signal and a separate directional coupler corresponding to each port of the network. Each directional coupler can be configured to link its corresponding port to the signal generator or to a load. Each directional coupler senses incident and reflected waves at the corresponding network port and passes signals to a data acquisition and processing (DAP) system representing magnitudes of the sensed incident and reflected waves.
In accordance with another aspect of the invention, the test system performs a set of calibration tests on itself. During each calibration test the wideband signal generator transmits the wideband signal to the load, ground or an open circuit via each the directional couplers and via both directional couplers connected in series. During these calibration tests, the DAP system frequency translates, amplifies, filters and digitizes the waveforms produced by the directional couplers, and subjects the resulting data to discrete Fourier transformation to produce frequency domain data representing the amplitude and phase of each frequency component of each of those waveforms. The test system computes error parameter E-parameters values for each frequency component of interest from the frequency domain data relating to that frequency of interest.
In accordance with a further aspect of the invention, the test system also tests the network by applying the wideband signal to each of its ports while terminating each other port with a load. During these tests the DAP system also frequency translates, amplifies, filters and digitizes the waveforms produced by the directional couplers, and subjects the resulting data to discrete Fourier transformation to produce frequency domain data representing the amplitude and phase of each frequency component of each of those waveforms. The DAP system them computes uncorrected S-parameters for each frequency component of interest from the frequency domain data relating to that frequency of interest.
In accordance with yet another aspect of the invention, the test system computes corrected S-parameters for the network for each frequency of interest as a function of the uncorrected S-parameters and computed E-parameters for that frequency of interest.
Since the calibration and network tests are performed using the wideband signal as stimulus, rather than single-frequency signals, the test conditions for the network more closely resemble the actual conditions under which the network is expected to operate. The calculated S-parameter values for each frequency of interest thus more accurately reflect network behavior than prior art single-frequency tests, particularly when the wideband signal drives the network into a non-linear operating region.
It is accordingly an object of the invention to provide a measurement system for accurately determining the S-parameters of a network such as an amplifier that is expected to be driven into a non-linear operating region by its input signal.
The concluding portion of this specification particularly points out and distinctly claims the subject matter of the present invention. However those skilled in the art will best understand both the organization and method of operation of the invention, together with further advantages and objects thereof, by reading the remaining portions of the specification in view of the accompanying drawing(s) wherein like reference characters refer to like elements.